WITHDRAWN: Rankin-Selberg Euler systems and p-adic interpolation. arXiv:1405.3079
Preprint, arXiv:1405.3079 [math.NT] (2014); retraction notice ibid.
Editorial note: This arXiv submission has been withdrawn.
Summary: We construct motivic cohomology classes attached to Rankin–Selberg convolutions of modular forms of weights \(\ge 2\), show that these vary analytically in p-adic families, and relate their image under the p-adic regulator map to values of L-functions. As consequences, we prove new cases of Perrin-Riou’s conjecture on motivic L-values; we prove finiteness results for Tate–Shafarevich groups for twists of elliptic curves by dihedral Artin characters; and we prove one inclusion in the Iwasawa main conjecture for a single modular form over an imaginary quadratic field.
Summary: We construct motivic cohomology classes attached to Rankin–Selberg convolutions of modular forms of weights \(\ge 2\), show that these vary analytically in p-adic families, and relate their image under the p-adic regulator map to values of L-functions. As consequences, we prove new cases of Perrin-Riou’s conjecture on motivic L-values; we prove finiteness results for Tate–Shafarevich groups for twists of elliptic curves by dihedral Artin characters; and we prove one inclusion in the Iwasawa main conjecture for a single modular form over an imaginary quadratic field.
MSC:
| 11F85 | \(p\)-adic theory, local fields |
| 11F67 | Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols |
| 11G40 | \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture |
| 14G35 | Modular and Shimura varieties |
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